Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F

Applied Mathematics and Computation

Volumn 217, Issue 5, 2010, Pages 2191-2199

  Xie, Li ^a   Liu, Yanjun ^a   Yang, Huizhong ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Gradient search; Iterative algorithm; Least squares; Lyapunov matrix equations; Sylvester matrix equations

Indexed keywords

GRADIENT SEARCH; ITERATIVE ALGORITHM; LEAST SQUARE; LYAPUNOV MATRIX EQUATIONS; SYLVESTER MATRIX EQUATIONS;

ALGORITHMS; MATRIX ALGEBRA;

ITERATIVE METHODS;

EID: 77957293938     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.07.019     Document Type: Article

References (46)

1. F. Ding, and T. Chen Gradient based iterative algorithms for solving a class of matrix equations IEEE Transactions on Automatic Control 50 8 2005 1216 1221
2. F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Systems and Control Letters 54 2 2005 95 107
3. F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM Journal on Control and Optimization 44 6 2006 2269 2284
4. F. Ding, P.X. Liu, and J. Ding Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle Applied Mathematics and Computation 197 1 2008 41 50
5. Y. Shi, F. Ding, and T. Chen 2-Norm based recursive design of transmultiplexers with designable filter length Circuits, Systems, and Signal Processing 25 4 2006 447 462
6. D.Q. Wang, and F. Ding Input-output data filtering based recursive least squares identification for CARARMA systems Digital Signal Processing 20 4 2010 991 999
7. Y.J. Liu, L. Yu, and F. Ding Multi-innovation extended stochastic gradient algorithm and its performance analysis Circuits, Systems and Signal Processing 29 4 2010 649 667
8. F. Ding, P. X Liu, and G. Liu Multi-innovation least squares identification for linear and pseudo-linear regression models IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40 3 2010 767 778
9. F. Ding, Y. Shi, and T. Chen Performance analysis of estimation algorithms of non-stationary ARMA processes IEEE Transactions on Signal Processing 54 3 2006 1041 1053
10. F. Ding, P.X. Liu, and G. Liu Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises Signal Processing 89 10 2009 1883 1890
11. F. Ding, and T. Chen Performance analysis of multi-innovation gradient type identification methods Automatica 43 1 2007 1 14
12. F. Ding Several multi-innovation identification methods Digital Signal Processing 20 4 2010 1027 1039
13. D.Q. Wang, and F. Ding Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems Digital Signal Processing 20 3 2010 750 762
14. M. Dehghan, and M. Hajarian An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation Applied Mathematics and Computation 202 2 2008 571 588
15. A. Kilicman, and Z. Al Zhour Vector least-squares solutions for coupled singular matrix equations Journal of Computational and Applied Mathematics 206 2 2007 1051 1069
16. F. Ding Transformations between some special matrices Computers and Mathematics with Applications 59 8 2010 2676 2695
17. Z.L. Tian, and C.Q. Gu A numerical algorithm for Lyapunov equations Applied Mathematics and Computation 202 1 2008 44 53
18. F. Ding, P.X. Liu, and G. Liu Gradient based and least-squares based iterative identification methods for OE and OEMA systems Digital Signal Processing 20 3 2010 664 677
19. Y.J. Liu, D.Q. Wang, and F. Ding Least-squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data Digital Signal Processing 20 5 2010 1458 1467
20. D.Q. Wang, and F. Ding Gradient-based iterative parameter estimation for Box-Jenkins systems Computers and Mathematics with Applications 2010 10.1016/j.camwa.2010.06.001
21. Z.Y. Peng An iterative method for the least squares symmetric solution of the linear matrix equation AXB = C Applied Mathematics and Computation 170 1 2005 711 723
22. D.J. Evans, and M.M. Martins AOR method for AX -XB = C International Journal of Computer Mathematics 52 1-2 1994 75 82
23. U.B. Berlin, and P.B. Chemnitz Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic Computing 78 3 2006 211 234
24. P. Benner, E.S. Quintana-Ortí, and G. Quintana-Ortí Solving stable Sylvester equations via rational iterative schemes Journal of Scientific Computing 28 1 2006 51 83
25. F. Ding, and T. Chen Hierarchical gradient-based identification of multivariable discrete-time systems Automatica 41 2 2005 315 325 (Pubitemid 41536582)
26. F. Ding, and T. Chen Hierarchical least squares identification methods for multivariable systems IEEE Transactions on Automatic Control 50 3 2005 397 402 (Pubitemid 40448592)
27. H.Q. Han, L. Xie, F. Ding, and X.G. Liu Hierarchical least squares based iterative identification for multivariable systems with moving average noises Mathematical and Computer Modelling 51 9-10 2010 1213 1220
28. L. Xie, J. Ding, and F. Ding Gradient based iterative solutions for general linear matrix equations Computers and Mathematics with Applications 58 7 2009 1441 1448
29. J. Ding, Y.J. Liu, and F. Ding Iterative solutions to matrix equations of form AiXBi = Fi Computers and Mathematics with Applications 59 11 2010 3500 3507
30. L. Xie, H.Z. Yang, J. Ding, F. Ding, Gradient-based iterative solutions for general matrix equations, in: 2009 American Control Conference, June 10-12, 2009, St. Louis, MO, USA, pp. 500-505.
31. F. Ding System Identification Theory and Methods + Matlab Simulations 2010 China Electric Power Press Beijing (in Chinese)
32. F. Ding, H.B. Chen, and M. Li Multi-innovation least squares identification methods based on the auxiliary model for MISO systems Applied Mathematics and Computation 187 2 2007 658 668
33. L.L. Han, and F. Ding Multi-innovation stochastic gradient algorithms for multi-input multi-output systems Digital Signal Processing 19 4 2009 545 554
34. F. Ding, and T. Chen Identification of Hammerstein nonlinear ARMAX systems Automatica 41 9 2005 1479 1489
35. F. Ding, Y. Shi, and T. Chen Auxiliary model based least-squares identification methods for Hammerstein output-error systems Systems and Control Letters 56 5 2007 373 380 (Pubitemid 46435731)
36. D.Q. Wang, and F. Ding Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX Systems Computers and Mathematics with Applications 56 12 2008 3157 3164
37. D.Q. Wang, Y.Y. Chu, and F. Ding Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems Computers and Mathematics with Applications 59 9 2010 3092 3098
38. D.Q. Wang, Y.Y. Chu, G.W. Yang, and F. Ding Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems Mathematical and Computer Modelling 52 1-2 2010 309 317
39. F. Ding, X.P. Liu, and Y. Shi Convergence analysis of estimation algorithms of dual-rate stochastic systems Applied Mathematics and Computation 176 1 2006 245 261
40. F. Ding, P.X. Liu, and H.Z. Yang Parameter identification and intersample output estimation for dual-rate systems IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 38 4 2008 966 975
41. J. Ding, Y. Shi, H.G. Wang, and F. Ding A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems Digital Signal Processing 20 4 2010 1238 1249
42. F. Ding, L. Qiu, and T. Chen Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems Automatica 45 2 2009 324 332
43. Y.J. Liu, L. Xie, F. Ding, and An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering 223 4 2009 445 454
44. L. Xie, H.Z. Yang, and F. Ding Modeling and identification for non-uniformly periodically sampled-data systems IET Control Theory and Applications 4 5 2010 784 794
45. F. Ding, G. Liu, and X.P. Liu Partially coupled stochastic gradient identification methods for non-uniformly sampled systems IEEE Transaction on Automatic Control 55 8 2010 10.1109/TAC.2010.2050713
46. F. Ding, and J. Ding Least squares parameter estimation with irregularly missing data International Journal of Adaptive Control and Signal Processing 24 7 2010 540 553